Periodic gratings are typically used for process monitoring and control in the field of semiconductor manufacturing. The periodic gratings may be one or more lines fabricated in series on a substrate. For example, one typical use of periodic gratings includes fabricating a periodic grating in proximity to the operating structure of a semiconducting chip. The periodic grating is then illuminated with an electromagnetic radiation by a optical metrology tool. The electromagnetic radiation that deflects off of the periodic grating are collected as a diffraction signal. The diffraction signal is then analyzed to determine whether the periodic grating, and by extension whether the operating structure of the semiconductor chip, has been fabricated according to specifications.
In one conventional system, the diffraction signal collected from illumination of the periodic grating (the measured diffraction signal) is compared to a library of simulated diffraction signals. Each simulated diffraction signal in the library is associated with a hypothetical profile. When a match is made between the measured diffraction signal and one of the simulated diffraction signals in the library, the hypothetical profile associated with the simulated diffraction signal is presumed to represent the actual profile of the periodic grating.
The actual profile of the periodic grating may represent a series of features with very tightly controlled parameters, or critical dimensions. The critical dimension may be a line width, a space width, or a contact length. The series of features may be tightly arranged in dense regions and loosely arranged in isolated regions. A diffraction signal measured from a feature in an isolated region may be very different from a diffraction signal measured from a similarly-sized feature in a dense region.
The diffraction signal measured from an isolated structure in an isolated region is used to determine an isolated structure critical dimension (ICD). The diffraction signal measured from a dense structure in a dense region is used to determine a dense structure critical dimension (DCD). The difference between the isolated structure critical dimension (ICD) and the dense structure critical dimension (DCD) is known as the iso-dense bias (ΔIB),ΔIB=ICD−DCD 
The iso-dense bias is accounted for by the optical metrology tool so that similarly sized features may be measured consistently, independent of surrounding features. Currently, the iso-dense bias is determined by making at least one measurement of features in a dense region and a second measurement of features in an isolated region to find a difference between the isolated structure critical dimension (ICD) and the dense structure critical dimension (DCD). This requires consecutive measurements of at least one metrology grating target with isolated an line and one grating target with dense lines. The iso-dense bias is represented by the difference between these measurements. Calculating the iso-dense bias using this methodology requires multiple, time-consuming measurements by the optical metrology tool.